Kernel Consistent Density Equality Test with Mixed Data Types

npdeneqtest implements a consistent integrated squared difference test for equality of densities as described in Li, Maasoumi, and Racine (2009).

Usage

npdeneqtest(x = NULL,
            y = NULL,
            bw.x = NULL,
            bw.y = NULL,
            boot.num = 399,
            random.seed = 42,
            ...)

Arguments

Data, Bandwidth Inputs And Formula Interface

These arguments identify the two samples and any supplied bandwidths.

bw.x,bw.y: optional bandwidth objects for x,y
x,y: data frames for the two samples for which one wishes to test equality of densities. The variables in each data frame must be the same (i.e. have identical names).

Bootstrap Controls

These arguments control bootstrap replication and reproducibility settings.

boot.num: an integer value specifying the number of bootstrap replications to use. Defaults to 399.
random.seed: an integer used to seed R's random number generator. This is to ensure replicability. Defaults to 42.

Additional Arguments

Further arguments are passed to the bandwidth-selection routines used by the test.

...: additional arguments supplied to specify the bandwidth type, kernel types, and so on. This is used if you do not pass in bandwidth objects and you do not desire the default behaviours. To do this, you may specify any of bwscaling, bwtype, ckertype, ckerorder, ukertype, okertype.

Value

npdeneqtest returns an object of type deneqtest with the following components

Tn: the (standardized) statistic Tn
In: the (unstandardized) statistic In
Tn.bootstrap: contains the bootstrap replications of Tn
In.bootstrap: contains the bootstrap replications of In
Tn.P: the P-value of the Tn statistic
In.P: the P-value of the In statistic
boot.num: number of bootstrap replications

summary supports object of type deneqtest.

Book And Method Pointers

npdeneqtest compares two distributions by estimating the integrated squared difference between their density or probability functions. The two samples must have matching variables and data types because the statistic compares like with like.

For book-length background, see Li and Racine (2007), Chapter 12 Model Specification Tests, especially Section 12.2, and Chapter 13 Nonsmoothing Tests, especially Section 13.2. For density and mixed-data density context, see Racine (2019), Chapters 2 and 3.

References

Li, Q. and E. Maasoumi and J.S. Racine (2009), “A Nonparametric Test for Equality of Distributions with Mixed Categorical and Continuous Data,” Journal of Econometrics, 148, pp 186-200.

Author

Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca

Details

Documentation guide: see np.kernels for kernels, np.options for global options, and plot for plotting options.

npdeneqtest computes the integrated squared density difference between the estimated densities/probabilities of two samples having identical variables/datatypes. See Li, Maasoumi, and Racine (2009) for details.

Usage Issues

If you are using data of mixed types, then it is advisable to use the data.frame function to construct your input data and not cbind, since cbind will typically not work as intended on mixed data types and will coerce the data to the same type.

It is crucial that both data frames have the same variable names.

Examples

if (FALSE) { # \dontrun{
set.seed(1234)

## Distributions are equal

n <- 250

sample.A <- data.frame(x=rnorm(n))
sample.B <- data.frame(x=rnorm(n))

npdeneqtest(sample.A,sample.B,boot.num=99)

if (interactive()) Sys.sleep(5)

## Distributions are unequal

sample.A <- data.frame(x=rnorm(n))
sample.B <- data.frame(x=rchisq(n,df=5))

npdeneqtest(sample.A,sample.B,boot.num=99)

## Mixed datatypes, distributions are equal

sample.A <- data.frame(a=rnorm(n),b=factor(rbinom(n,2,.5)))
sample.B <- data.frame(a=rnorm(n),b=factor(rbinom(n,2,.5)))

npdeneqtest(sample.A,sample.B,boot.num=99)

if (interactive()) Sys.sleep(5)

## Mixed datatypes, distributions are unequal

sample.A <- data.frame(a=rnorm(n),b=factor(rbinom(n,2,.5)))
sample.B <- data.frame(a=rnorm(n,sd=10),b=factor(rbinom(n,2,.25)))

npdeneqtest(sample.A,sample.B,boot.num=99)
} # }